Warm-Up #1 1. 18 + (–25) = ? 2. 1 2 – 4 3 = ? ANSWER –7 2 3 ANSWER 1. 18 + (–25) = ? 2. 1 2 – 4 3 = ? ANSWER –7 2 3 ANSWER 3. What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F ? ANSWER 23º F

Real Numbers Real Numbers Natural (Counting) numbers: N = {1, 2, 3, …} Whole numbers: W = {0, 1, 2, 3, …} Integers: Z = {0, 1, 2, 3, …} Rational Numbers: Any number that can be written as a fraction where the numerator and denominator are both integers and the denominator doesn’t equal zero Irrational Numbers: Any number that isn’t a rational number Real Numbers Rational Numbers Irrational Numbers Integers -5 -2 -1 Whole Numbers Natural Numbers 1 2 3

Graph real numbers on a number line EXAMPLE 1 Graph real numbers on a number line Graph the real numbers – and 3 on a number line. 5 4 SOLUTION Note that – = –1.25. Use a calculator to approximate 3 to the nearest tenth: 5 4 3 1.7. (The symbol means is approximately equal to.) So, graph – between –2 and –1, and graph 3 between 1 and 2, as shown on the number line below. 5 4

EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. 7 + 4 = 4 + 7 SOLUTION Commutative property of addition 13 = 1 1 13 SOLUTION Inverse property of multiplication

GUIDED PRACTICE for Examples 3 and 4 Identify the property that the statement illustrates. (2 3) 9 = 2 (3 9) SOLUTION Associative property of multiplication. 15 + 0 = 15 SOLUTION Identity property of addition.

GUIDED PRACTICE for Examples 3 and 4 Identify the property that the statement illustrates. 4(5 + 25) = 4(5) + 4(25) SOLUTION Distributive property. 1 500 = 500 SOLUTION Identity property of multiplication.

EXAMPLE 1 Evaluate powers (–5)4 = (–5) (–5) (–5) (–5) = 625 –54 = –(5 5 5 5) = –625

Evaluate an algebraic expression Evaluate –4x2 – 6x + 11 when x = –3. EXAMPLE 2 Evaluate an algebraic expression Evaluate –4x2 – 6x + 11 when x = –3. –4x2 – 6x + 11 = –4(–3)2 – 6(–3) + 11 Substitute –3 for x. = –4(9) – 6(–3) + 11 Evaluate power. = –36 + 18 + 11 Multiply. = –7 Add.

Evaluate the expression. GUIDED PRACTICE for Examples 1, 2, and 3 Evaluate the expression. 63 SOLUTION 216 –26 SOLUTION –64

GUIDED PRACTICE for Examples 1, 2, and 3 (–2)6 SOLUTION 64 5x(x – 2) when x = 6 SOLUTION 120

GUIDED PRACTICE for Examples 1, 2, and 3 3y2 – 4y when y = – 2 SOLUTION 20 (z + 3)3 when z = 1 SOLUTION 64

Simplify by combining like terms EXAMPLE 4 Simplify by combining like terms 8x + 3x = (8 + 3)x Distributive property = 11x Add coefficients. 5p2 + p – 2p2 = (5p2 – 2p2) + p Group like terms. = 3p2 + p Combine like terms. 3(y + 2) – 4(y – 7) = 3y + 6 – 4y + 28 Distributive property = (3y – 4y) + (6 + 28) Group like terms. = –y + 34 Combine like terms.

Simplify by combining like terms EXAMPLE 4 Simplify by combining like terms 2x – 3y – 9x + y = (2x – 9x) + (– 3y + y) Group like terms. = –7x – 2y Combine like terms.

GUIDED PRACTICE for Example 5 8. Identify the terms, coefficients, like terms, and constant terms in the expression 2 + 5x – 6x2 + 7x – 3. Then simplify the expression. SOLUTION Terms: 2, 5x, –6x2 , 7x, –3 Coefficients: 5 from 5x, –6 from –6x2 , 7 from 7x Like terms: 5x and 7x, 2 and –3 Constants: 2 and –3 Simplify: –6x2 +12x – 1

Simplify the expression. GUIDED PRACTICE for Example 5 Simplify the expression. 15m – 9m SOLUTION 6m 2n – 1 + 6n + 5 SOLUTION 8n + 4

GUIDED PRACTICE for Example 5 3p3 + 5p2 – p3 SOLUTION 2p3 + 5p2 2q2 + q – 7q – 5q2 SOLUTION –3q2 – 6q

GUIDED PRACTICE for Example 5 8(x – 3) – 2(x + 6) SOLUTION 6x – 36 –4y – x + 10x + y SOLUTION 9x –3y

Classwork 1.1/1.2 WS 1.1 (2-18 even) WS 1.2 (2-26 even)

In the Practice Workbook: Homework 1.1/1.2 In the Practice Workbook: WS 1.1 (1-19 odd) WS 1.2 (1-21 odd)